Kernel Geometric Mean Metric Learning

Abstract

Geometric mean metric learning (GMML) algorithm is a novel metric learning approach proposed recently. It has many advantages such as unconstrained convex objective function, closed form solution, faster computational speed, and interpretability over other existing metric learning technologies. However, addressing the nonlinear problem is not effective enough. The kernel method is an effective method to solve nonlinear problems. Therefore, a kernel geometric mean metric learning (KGMML) algorithm is proposed. The basic idea is to transform the input space into a high-dimensional feature space through nonlinear transformation, and use the integral representation of the weighted geometric mean and the Woodbury matrix identity in new feature space to generalize the analytical solution obtained in the GMML algorithm as a form represented by a kernel matrix, and then the KGMML algorithm is obtained through operations. Experimental results on 15 datasets show that the proposed algorithm can effectively improve the accuracy of the GMML algorithm and other metric algorithms.